Vincen wrote: ↑Fri May 28, 2021 6:55 am
How many times will the digit 7 be written when listing the integers from 1 to 1000?
(A) 110
(B) 111
(C) 271
(D) 300
(E) 304
Answer:
D
Source: GMAT Club Tests
Here's one way to look at it.
Write all of the numbers as
3-digit numbers.
That is, 000, 001, 002, 003, .... 998, 999
NOTE: Yes, I have started at 000 and ended at 999, even though though the question asks us to look at the numbers from 1 to 1000. HOWEVER, notice that 000 and 1000 do not have any 7's so the outcome will be the same.
First, there are 1000 integers from 000 to 999
There are 3 digits in each integer.
So, there is a TOTAL of
3000 individual digit. (since 1000 x 3 = 3000)
Each of the 10 digits is equally represented, so the 7 will account for 1/10 of all digits.
1/10 of
3000 = 300
So, there are 300 0's, 300 1's, 300 2's, 300 3's, . . ., and 300 9's in the integers from 000 to 999
Answer: D
Cheers,
Bren
